Robust H∞ control with multiple constraints for the track-following system of an optical disk drive

In this paper, we design a tracking controller which satisfies transient response specifications and maintains tracking error within a tolerable limit for the uncertain track-following system of an optical disk drive. To this end, a robust H1 control problem with regional stability constraints and sinusoidal disturbance rejection is considered. The internal model principle is used for rejecting the sinusoidal disturbance caused by eccentric rotation of the disk. We show that a condition satisfying the regional stability constraints can be expressed in terms of a linear matrix inequality (LMI) using the Lyapunov theory and S-procedure. Finally, a tracking controller is obtained by solving an LMI optimization problem involving two LMI’s. The proposed controller design method is evaluated through an experiment.